scipy.special.roots_sh_chebyu

scipy.special.roots_sh_chebyu(n, mu=False)

Gauss-Chebyshev (second kind, shifted) quadrature.

Computes the sample points and weights for Gauss-Chebyshev quadrature. The sample points are the roots of the n-th degree shifted Chebyshev polynomial of the second kind, \(U_n(x)\). These sample points and weights correctly integrate polynomials of degree \(2n - 1\) or less over the interval \([0, 1]\) with weight function \(f(x) = \sqrt{x - x^2}\).

Parameters

nint

quadrature order

mubool, optional

If True, return the sum of the weights, optional.

Returns

xndarray

Sample points

wndarray

Weights

mufloat

Sum of the weights

See also

scipy.integrate.quadrature

scipy.integrate.fixed_quad